Modern day applications require use of multi-processor systems for reasons of scalability and power efficiency. As more and more applications are integrated on a single device, mapping and analyzing them on a multi-processor system becomes a multi-dimensional problem. Each possible set of applications that can be active simultaneously leads to a different use-case (also referred to as scenario) that the system has to be verified and tested for. Analyzing the feasibility and resource utilization of all possible use-cases is very demanding and often infeasible. In this paper, we highlight the issue of composability, i.e. being able to analyze applications in isolation while still reason about their overall behavior. We observe that arbitration plays an important role in this analysis. We compare two simple, yet commonly used arbitration mechanisms, and highlight the properties that are important for such analysis. We conclude that none of these arbitration mechanism is ideal for such an analysis and propose some variations to make them more suited for the analysis.